Sonic Thermometry
Prepared By:
Applied Technologies, Inc.
950 S. Sherman St. Unit B
Longmont, CO 80501
Sonic Thermometry
Sonic anemometers have had extensive use in the scientific community. These instruments are
used to measure atmospheric parameters that most rotating instruments cannot. Wind speed and
wind direction or individual axes of wind velocity are most commonly measured. Along with
these measurements, another parameter can be extracted from the sonic anemometer (i.e.), sonic
temperature.
Since the transit time measurement method is used by sonic anemometers for wind, it is
independent of temperature, relative humidity, and pressure. The common method of computing
wind velocities is:
V = d/2 (1/t1 - 1/t2)
(1)
Where t1 ant t2 are transit times in the opposing directions, d is the distance
between the transducers.
In order to determine the distance between transducers, it is necessary to calibrate the sonic
anemometer, using a zero-air chamber placed over the instrument axis to be calibrated and
inserting a temperature probe into the zero-air chamber. Since there is theoretically no wind
movement, the transit times will be effectively equal. One can then compute the speed of sound
by:
C = (γRT/Md)1/2
(2)
Where γ is the ratio of Cd and Cv of dry air, (1.4 is commonly used), R is the
universal gas constant, latest value 8314.51 (N·m/kmol·K), T is the temperature of calibration in
Kelvin, and Md is the mol value of dry air (28.954812).
From the transit times of the sonic anemometer, the speed of sound can be computed as follows:
C2 = d2/4 (1/t1 + 1/t2)2 + Vn2,
(3)
Vn2 is the crosswind contamination component
Substituting the calibration speed of sound into the above equation, it can be solved for d the
distance between transducers. This d value remains stored in the anemometer memory until the
unit is recalibrated.
In most three axis sonic anemometers, of u, v, w, the w axis is the axis normally chosen to
represent the sonic temperature. It is also worth noting that in many tri-axis sonic anemometers,
the w component is not directly measured, but is algebraically derived from tilted axes. A recent
paper published in the June 6, 2012 issue of Journal of Boundary-Layer Meteorology, titled
“How Well Can We Measure the Vertical Wind Speed? Implications for Fluxes of Energy and
Mass”, discussed that research-grade three-dimensional sonic anemometers, currently in use,
should be redesigned to minimize sine errors by measuring the vertical wind speed using one
pair of vertically aligned transducers. The conclusion of this study was that estimates of w from
one pair of vertically aligned transducers experienced negligible angle-of-attack errors at typical
flux angles.
The sonic temperature parameter along with velocity values of the vertical axis (w) are used to
compute momentum flux, sensible heat flux and friction velocity. For these flux measurements,
the absolute value of the sonic temperature is not necessary. The fluctuations at 10 Hz or more is
the primary factor. Other atmospheric parameters can be determined by using the sonic
anemometer with conjoined instruments.
For a two-axis sonic anemometer, the measurement of the wind velocities in the horizontal plane
is the primary usage. One or both of these axes can be used to determine the sonic temperature
as derived in the above equations. The axis used to determine the speed-of-sound cannot be the
axis used to supply crosswind contamination values.
For a requirement to measure absolute or ambient temperature, it should be noted that the
calibration was accomplished using dry air as the denominator in equation (2). Kaimal, 1990,
(Another Look at Sonic Thermometry), has shown the sonic temperature measurement is subject
to errors due to the humidity in the air.
C2 = 403T (1+0.32e/P)
(4)
Where 403 is the product of γR/Md, this value has been since upgraded by ATI to
reflect the latest R and Md, (401.8778). The value of CO2 has since risen to 394.5 ppm,
increasing the molecular weight of dry air. The factor e is the vapor pressure of water and P is
the atmospheric pressure in Pa.
Dr. Kaimal, has shown that, discounting the effects of humidity, for a calculation of atmospheric
temperature from sonic temperature can be erroneous by as much as 2.4º C. This effect is
computed from his paper,
Ts = T (1 + 0.32 e/P)
(5)
The value 0.32 has been upgraded to 0.3279 because of change in molecular weight of dry air.
The altitude that the sonic anemometer is operating (i.e.) pressure cannot be predicted, so 920
kPa was chosen as a median pressure between Boulder, CO and sea level. Plotting equation (5)
at 20º C for T shows a negative slope of -0.024, indicating the possible error of 2.4º C at 100
percent humidity. The sonic anemometer temperature (Ts) will always be high due to the amount
of humidity in the air.
By applying an algorithm to the sonic temperature computed, a value of the atmospheric air can
be obtained with some degree of accuracy.
ATI Temperature Calculation
ATI has for some time understood the effect of humidity on the calculation of atmospheric
temperature from sonic temperature. One of the choices of our instrument is the capability of
inserting a known humidity factor when calibrating. When calibrating the instrument the
software asks for “Temp C” the temperature inside the zero-air chamber. When a value is
inserted, a second query asks for “RH”. At this point an operator may insert the humidity that is
closest to that inside the zero-air chamber.
The calibration, when complete, has computed a “d” commensurate with a known value of
humidity. If this same humidity were encountered in the outside atmosphere, the value returned
for sonic temperature will be the same as that temperature inserted in calibration.
Another feature of the ATI sonic anemometer is that a menu selection allows the operator to
choose the relative humidity, in which the instrument will be operating, from 0 to 100 percent. If
50 percent were chosen, this adjusts the sonic temperature due to relative humidity to a midrange of 0 to -2.4º C. The error of calculation is now halved to 1.2º C or ±0.6º C. If the outside
relative humidity does not deviate much from the 50%, the error is probably much less. By this
means, the ATI sonic anemometer can provide nearly-accurate temperature of the outside
environment, lessening any post-operation data correction.
For comparing sonic anemometers, the ATI sonic anemometer could be used as a standard to
which others are compared. Again, referring to the Journal of Boundary-Layer Meteorology
paper discussed earlier, some of the sonic anemometers used in scientific study are examined.